Distributed finite‐time control for systems interconnected over an undirected graph

Abstract

In this paper, the distributed finite-time control problem for the class of systems interconnected over an undirected graph is considered. First, the concepts of well-posedness, finite-time boundedness, and contractiveness for the considered systems are given. Then, a sufficient condition is developed to ensure that the plant is well-posed, finite-time bounded, and contractive, where the results are stated by terms of linear matrix inequalities (LMIs). For the control synthesis, we construct a distributed dynamic output-feedback controller inheriting the structure of the plant such that the resulting closed-loop system is finite-time bounded and contractive. Since the analysis condition of the plant used for the closed-loop system is presented by some nonlinear inequalities in given finite-time interval, we further derive a sufficient condition in terms of LMIs with some fixed parameter for the existence of an appropriate output-feedback controller such that the closed-loop system is contractive. Finally, numerical simulations are provided to show the validity of the proposed results.

Adaptive sliding mode observers‐based dissipative Hamilton finite time optimization control for the speed and tension system of reversible cold strip rolling mill

“…By above References 4–10, we can see most of them can only achieve asymptotic convergences, that is, the system states converged to the origin or the neighborhoods of origin only when $$$ t\to \infty $$$, while it is not easy to fulfill the requirements on quicker convergence rate and higher steady‐state accuracy in fact. Recently, finite time control method 11 appeared with the rapid development of homogeneous theory, which can make the system states converge in finite time. For example, Zhang et al 12 designed a finite time controller for a PMSM based on super‐twisting algorithm, which realized finite time control without speed sensor, and effectively improved system's dynamic performance and stability performance.…”

“…In addition, most References 4–14 adopted the cut and try method when tuning the controller parameters, however, this setting method relies on the people's debugging experience, and the whole process is cumbersome. To fully utilize the control potential of the given methods, the intelligent optimization algorithms can be adopted to optimize the controller parameters.…”